sin(2x)+cos(2x)=sqrt(1)
you did this correct
2sin(x)cos(x)-2sin^2(x)=0
2(sin(x)cos(x)-sin^2(x))=0..........to make it simple, here you need to factor out sin(x)
2sin(x)(cos(x)-sin(x))=0
if 2sin(x)=0 =>x = π n, n element Z
or
if cos(x)-sin(x)=0->cos(x)=sin(x) =>x = (1/4 )(4π n + π), n element Z or π n+π/4
